Tabletop extreme ultraviolet reflectometer for quantitative nanoscale reflectometry, scatterometry, and imaging

Imaging using coherent extreme-ultraviolet (EUV) light provides exceptional capabilities for the characterization of the composition and geometry of nanostructures by probing with high spatial resolution and elemental specificity. We present a multi-modal tabletop EUV imaging reflectometer for high-fidelity metrology of nanostructures. The reflectometer is capable of measurements in three distinct modes: intensity reflectometry, scatterometry, and imaging reflectometry, where each mode addresses different nanostructure characterization challenges. We demonstrate the system's unique ability to quantitatively and non-destructively measure the geometry and composition of nanostructures with tens of square microns field of view and sub-nanometer precision. Parameters such as surface and line edge roughness, density, nanostructure linewidth, and profile, as well as depth-resolved composition, can be quantitatively determined. The results highlight the applicability of EUV metrology to address a wide range of semiconductor and materials science challenges.

Optically controlling the competition between spin flips and intersite spin transfer in a Heusler half-metal on sub-100-fs time scales

The direct manipulation of spins via light may provide a path toward ultrafast energy-efficient devices. However, distinguishing the microscopic processes that can occur during ultrafast laser excitation in magnetic alloys is challenging. Here, we study the Heusler compound Co2MnGa, a material that exhibits very strong light-induced spin transfers across the entire M-edge. By combining the element specificity of extreme ultraviolet high-harmonic probes with time-dependent density functional theory, we disentangle the competition between three ultrafast light-induced processes that occur in Co2MnGa: same-site Co-Co spin transfer, intersite Co-Mn spin transfer, and ultrafast spin flips mediated by spin-orbit coupling. By measuring the dynamic magnetic asymmetry across the entire M-edges of the two magnetic sublattices involved, we uncover the relative dominance of these processes at different probe energy regions and times during the laser pulse. Our combined approach enables a comprehensive microscopic interpretation of laser-induced magnetization dynamics on time scales shorter than 100 femtoseconds.

Direct Observation of Enhanced Electron-Phonon Coupling in Copper Nanoparticles in the Warm-Dense Matter Regime

Warm dense matter (WDM) represents a highly excited state that lies at the intersection of solids, plasmas, and liquids and that cannot be described by equilibrium theories. The transient nature of this state when created in a laboratory, as well as the difficulties in probing the strongly coupled interactions between the electrons and the ions, make it challenging to develop a complete understanding of matter in this regime. In this work, by exciting isolated ∼8  nm copper nanoparticles with a femtosecond laser below the ablation threshold, we create uniformly excited WDM. Using photoelectron spectroscopy, we measure the instantaneous electron temperature and extract the electron-ion coupling of the nanoparticle as it undergoes a solid-to-WDM phase transition. By comparing with state-of-the-art theories, we confirm that the superheated nanoparticles lie at the boundary between hot solids and plasmas, with associated strong electron-ion coupling. This is evidenced both by a fast energy loss of electrons to ions, and a strong modulation of the electron temperature induced by strong acoustic breathing modes that change the nanoparticle volume. This work demonstrates a new route for experimental exploration of the exotic properties of WDM.

Numerical investigation of gas-filled multipass cells in the enhanced dispersion regime for clean spectral broadening and pulse compression

We show via numerical simulations that the regime of enhanced frequency chirp can be achieved in gas-filled multipass cells. Our results demonstrate that there exists a region of pulse and cell parameters for which a broad and flat spectrum with a smooth parabolic-like phase can be generated. This spectrum is compatible with clean ultrashort pulses, whose secondary structures are always below the 0.5% of its peak intensity such that the energy ratio (the energy contained within the main peak of the pulse) is above 98%. This regime makes multipass cell post-compression one of the most versatile schemes to sculpt a clean intense ultrashort optical pulse.

Universal Behavior of Highly Confined Heat Flow in Semiconductor Nanosystems: From Nanomeshes to Metalattices

Nanostructuring on length scales corresponding to phonon mean free paths provides control over heat flow in semiconductors and makes it possible to engineer their thermal properties. However, the influence of boundaries limits the validity of bulk models, while first-principles calculations are too computationally expensive to model real devices. Here we use extreme ultraviolet beams to study phonon transport dynamics in a 3D nanostructured silicon metalattice with deep nanoscale feature size and observe dramatically reduced thermal conductivity relative to bulk. To explain this behavior, we develop a predictive theory wherein thermal conduction separates into a geometric permeability component and an intrinsic viscous contribution, arising from a new and universal effect of nanoscale confinement on phonon flow. Using experiments and atomistic simulations, we show that our theory applies to a general set of highly confined silicon nanosystems, from metalattices, nanomeshes, porous nanowires, to nanowire networks, of great interest for next-generation energy-efficient devices.

Three-dimensional topological magnetic monopoles and their interactions in a ferromagnetic meta-lattice

Topological magnetic monopoles (TMMs), also known as hedgehogs or Bloch points, are three-dimensional (3D) non-local spin textures that are robust to thermal and quantum fluctuations due to the topology protection^1-4. Although TMMs have been observed in skyrmion lattices^1,5, spinor Bose-Einstein condensates^6,7, chiral magnets⁸, vortex rings^2,9 and vortex cores¹⁰, it has been difficult to directly measure the 3D magnetization vector field of TMMs and probe their interactions at the nanoscale. Here we report the creation of 138 stable TMMs at the specific sites of a ferromagnetic meta-lattice at room temperature. We further develop soft X-ray vector ptycho-tomography to determine the magnetization vector and emergent magnetic field of the TMMs with a 3D spatial resolution of 10 nm. This spatial resolution is comparable to the magnetic exchange length of transition metals¹¹, enabling us to probe monopole-monopole interactions. We find that the TMM and anti-TMM pairs are separated by 18.3 ± 1.6 nm, while the TMM and TMM, and anti-TMM and anti-TMM pairs are stabilized at comparatively longer distances of 36.1 ± 2.4 nm and 43.1 ± 2.0 nm, respectively. We also observe virtual TMMs created by magnetic voids in the meta-lattice. This work demonstrates that ferromagnetic meta-lattices could be used as a platform to create and investigate the interactions and dynamics of TMMs. Furthermore, we expect that soft X-ray vector ptycho-tomography can be broadly applied to quantitatively image 3D vector fields in magnetic and anisotropic materials at the nanoscale.

Super-resolved time–frequency measurements of coupled phonon dynamics in a 2D quantum material

Methods to probe and understand the dynamic response of materials following impulsive excitation are important for many fields, from materials and energy sciences to chemical and neuroscience. To design more efficient nano, energy, and quantum devices, new methods are needed to uncover the dominant excitations and reaction pathways. In this work, we implement a newly-developed superlet transform—a super-resolution time-frequency analytical method—to analyze and extract phonon dynamics in a laser-excited two-dimensional (2D) quantum material. This quasi-2D system, 1T-TaSe2, supports both equilibrium and metastable light-induced charge density wave (CDW) phases mediated by strongly coupled phonons. We compare the effectiveness of the superlet transform to standard time-frequency techniques. We find that the superlet transform is superior in both time and frequency resolution, and use it to observe and validate novel physics. In particular, we show fluence-dependent changes in the coupled dynamics of three phonon modes that are similar in frequency, including the CDW amplitude mode, that clearly demonstrate a change in the dominant charge-phonon couplings. More interestingly, the frequencies of the three phonon modes, including the strongly-coupled CDW amplitude mode, remain time- and fluence-independent, which is unusual compared to previously investigated materials. Our study opens a new avenue for capturing the coherent evolution and couplings of strongly-coupled materials and quantum systems.

Nonlinear post-compression in multi-pass cells in the mid-IR region using bulk materials

We numerically investigate the regime of nonlinear pulse compression at mid-IR wavelengths in a multi-pass cell (MPC) containing a dielectric plate. This post-compression setup allows for ionization-free spectral broadening and self-compression while mitigating self-focusing effects. We find that self-compression occurs for a wide range of MPC and pulse parameters and derive scaling rules that enable its optimization. We also reveal the solitonic dynamics of the pulse propagation in the MPC and its limitations and show that spatiotemporal/spectral couplings can be mitigated for appropriately chosen parameters. In addition, we reveal the formation of spectral features akin to quasi-phase matched degenerate four-wave mixing. Finally, we present two case studies of self-compression at 3-μm and 6-μm wavelengths using pulse parameters compatible with driving high-field physics experiments. The simulations presented in this paper set a framework for future experimental work using few-cycle pulses at mid-IR wavelengths.

Structural and Elastic Properties of Empty-Pore Metalattices Extracted via Nondestructive Coherent Extreme UV Scatterometry and Electron Tomography

Semiconductor metalattices consisting of a linked network of three-dimensional nanostructures with periodicities on a length scale <100 nm can enable tailored functional properties due to their complex nanostructuring. For example, by controlling both the porosity and pore size, thermal transport in these phononic metalattices can be tuned, making them promising candidates for efficient thermoelectrics or thermal rectifiers. Thus, the ability to characterize the porosity, and other physical properties, of metalattices is critical but challenging, due to their nanoscale structure and thickness. To date, only metalattices with high porosities, close to the close-packing fraction of hard spheres, have been studied experimentally. Here, we characterize the porosity, thickness, and elastic properties of a low-porosity, empty-pore silicon metalattice film (∼500 nm thickness) with periodic spherical pores (∼tens of nanometers), for the first time. We use laser-driven nanoscale surface acoustic waves probed by extreme ultraviolet scatterometry to nondestructively measure the acoustic dispersion in these thin silicon metalattice layers. By comparing the data to finite element models of the metalattice sample, we can extract Young's modulus and porosity. Moreover, by controlling the acoustic wave penetration depth, we can also determine the metalattice layer thickness and verify the substrate properties. Additionally, we utilize electron tomography images of the metalattice to verify the geometry and validate the porosity extracted from scatterometry. These advanced characterization techniques are critical for informed and iterative fabrication of energy-efficient devices based on nanostructured metamaterials.

Single-Frame Characterization of Ultrafast Pulses with Spatiotemporal Orbital Angular Momentum

Light that carries spatiotemporal orbital angular momentum (ST-OAM) makes possible new types of optical vortices arising from transverse OAM. ST-OAM pulses exhibit novel properties during propagation, transmission, refraction, diffraction, and nonlinear conversion, attracting growing experimental and theoretical interest and studies. However, one major challenge is the lack of a simple and straightforward method for characterizing ultrafast ST-OAM pulses. Using spatially resolved spectral interferometry, we demonstrate a simple, stationary, single-frame method to quantitatively characterize ultrashort light pulses carrying ST-OAM. Using our method, the presence of an ST-OAM pulse, including its main characteristics such as topological charge numbers and OAM helicity, can be identified easily from the unique and unambiguous features directly seen on the raw data-without any need for a full analysis of the data. After processing and reconstructions, other exquisite features, including pulse dispersion and beam divergence, can also be fully characterized. Our fast characterization method allows high-throughput and quick feedback during the generation and optical alignment processes of ST-OAM pulses. It is straightforward to extend our method to single-shot measurement by using a high-speed camera that matches the pulse repetition rate. This new method can help advance the field of spatially and temporally structured light and its applications in advanced metrologies.

Temporal and spectral multiplexing for EUV multibeam ptychography with a high harmonic light source

We demonstrate temporally multiplexed multibeam ptychography implemented for the first time in the EUV, by using a high harmonic based light source. This allows for simultaneous imaging of different sample areas, or of the same area at different times or incidence angles. Furthermore, we show that this technique is compatible with wavelength multiplexing for multibeam spectroscopic imaging, taking full advantage of the temporal and spectral characteristics of high harmonic light sources. This technique enables increased data throughput using a simple experimental implementation and with high photon efficiency.

High-resolution, wavefront-sensing, full-field polarimetry of arbitrary beams using phase retrieval

Recent advances in structured illumination are enabling a wide range of applications from imaging to metrology, which can benefit from advanced beam characterization techniques. Solving uniquely for the spatial distribution of polarization in a beam typically involves the use of two or more polarization optics, such as a polarizer and a waveplate, which is prohibitive for some wavelengths outside of the visible spectrum. We demonstrate a technique that circumvents the use of a waveplate by exploiting extended Gerchberg-Saxton phase retrieval to extract the phase. The technique enables high-resolution, wavefront-sensing, full-field polarimetry capable of solving for both simple and exotic polarization states, and moreover, is extensible to shorter wavelength light.

Necklace-structured high-harmonic generation for low-divergence, soft x-ray harmonic combs with tunable line spacing

The extreme nonlinear optical process of high-harmonic generation (HHG) makes it possible to map the properties of a laser beam onto a radiating electron wave function and, in turn, onto the emitted x-ray light. Bright HHG beams typically emerge from a longitudinal phased distribution of atomic-scale quantum antennae. Here, we form a transverse necklace-shaped phased array of linearly polarized HHG emitters, where orbital angular momentum conservation allows us to tune the line spacing and divergence properties of extreme ultraviolet and soft x-ray high-harmonic combs. The on-axis HHG emission has extremely low divergence, well below that obtained when using Gaussian driving beams, which further decreases with harmonic order. This work provides a new degree of freedom for the design of harmonic combs-particularly in the soft x-ray regime, where very limited options are available. Such harmonic beams can enable more sensitive probes of the fastest correlated charge and spin dynamics in molecules, nanoparticles, and materials.

Supercontinuum generation in the enhanced frequency chirp regime in multipass cells

We identify, via numerical simulations, the regime of enhanced frequency chirp during nonlinear propagation in multipass cell. This regime - used before the dawn of chirped pulse amplification to generate ultrashort pulses - paves the way for the generation of temporally clean few-cycle pulses. Here, we demonstrate numerically that the spectra of pulses from an Yb-based laser system can be broadened into a flat supercontinuum with a smooth spectral phase compatible with a clean few-cycle pulse with temporal secondary structures with peak intensity below 0.5% that of the main peak.

Creation of a novel inverted charge density wave state

Charge density wave (CDW) order is an emergent quantum phase that is characterized by periodic lattice distortion and charge density modulation, often present near superconducting transitions. Here, we uncover a novel inverted CDW state by using a femtosecond laser to coherently reverse the star-of-David lattice distortion in 1T-TaSe₂. We track the signature of this novel CDW state using time- and angle-resolved photoemission spectroscopy and the time-dependent density functional theory to validate that it is associated with a unique lattice and charge arrangement never before realized. The dynamic electronic structure further reveals its novel properties that are characterized by an increased density of states near the Fermi level, high metallicity, and altered electron-phonon couplings. Our results demonstrate how ultrafast lasers can be used to create unique states in materials by manipulating charge-lattice orders and couplings.

Bright, single helicity, high harmonics driven by mid-infrared bicircular laser fields

High-harmonic generation (HHG) is a unique tabletop light source with femtosecond-to-attosecond pulse duration and tailorable polarization and beam shape. Here, we use counter-rotating femtosecond laser pulses of 0.8 µm and 2.0 μm to extend the photon energy range of circularly polarized high-harmonics and also generate single-helicity HHG spectra. By driving HHG in helium, we produce circularly polarized soft x-ray harmonics beyond 170 eV-the highest photon energy of circularly polarized HHG achieved to date. In an Ar medium, dense spectra at photon energies well beyond the Cooper minimum are generated, with regions composed of a single helicity-consistent with the generation of a train of circularly polarized attosecond pulses. Finally, we show theoretically that circularly polarized HHG photon energies can extend beyond the carbon K edge, extending the range of molecular and materials systems that can be accessed using dynamic HHG chiral spectro-microscopies.

A General and Predictive Understanding of Thermal Transport from 1D- and 2D-Confined Nanostructures: Theory and Experiment

Heat management is crucial in the design of nanoscale devices as the operating temperature determines their efficiency and lifetime. Past experimental and theoretical works exploring nanoscale heat transport in semiconductors addressed known deviations from Fourier's law modeling by including effective parameters, such as a size-dependent thermal conductivity. However, recent experiments have qualitatively shown behavior that cannot be modeled in this way. Here, we combine advanced experiment and theory to show that the cooling of 1D- and 2D-confined nanoscale hot spots on silicon can be described using a general hydrodynamic heat transport model, contrary to previous understanding of heat flow in bulk silicon. We use a comprehensive set of extreme ultraviolet scatterometry measurements of nondiffusive transport from transiently heated nanolines and nanodots to validate and generalize our ab initio model, that does not need any geometry-dependent fitting parameters. This allows us to uncover the existence of two distinct time scales and heat transport mechanisms: an interface resistance regime that dominates on short time scales and a hydrodynamic-like phonon transport regime that dominates on longer time scales. Moreover, our model can predict the full thermomechanical response on nanometer length scales and picosecond time scales for arbitrary geometries, providing an advanced practical tool for thermal management of nanoscale technologies. Furthermore, we derive analytical expressions for the transport time scales, valid for a subset of geometries, supplying a route for optimizing heat dissipation.

Coherent Fourier scatterometry using orbital angular momentum beams for defect detection

Defect inspection on lithographic substrates, masks, reticles, and wafers is an important quality assurance process in semiconductor manufacturing. Coherent Fourier scatterometry (CFS) using laser beams with a Gaussian spatial profile is the standard workhorse routinely used as an in-line inspection tool to achieve high throughput. As the semiconductor industry advances toward shrinking critical dimensions in high volume manufacturing using extreme ultraviolet lithography, new techniques that enable high-sensitivity, high-throughput, and in-line inspection are critically needed. Here we introduce a set of novel defect inspection techniques based on bright-field CFS using coherent beams that carry orbital angular momentum (OAM). One of these techniques, the differential OAM CFS, is particularly unique because it does not rely on referencing to a pre-established database in the case of regularly patterned structures with reflection symmetry. The differential OAM CFS exploits OAM beams with opposite wavefront or phase helicity to provide contrast in the presence of detects. We numerically investigated the performance of these techniques on both amplitude and phase defects and demonstrated their superior advantages-up to an order of magnitude higher in signal-to-noise ratio-over the conventional Gaussian beam CFS. These new techniques will enable increased sensitivity and robustness for in-line nanoscale defect inspection and the concept could also benefit x-ray scattering and scatterometry in general.

Nondestructive, high-resolution, chemically specific 3D nanostructure characterization using phase-sensitive EUV imaging reflectometry

Next-generation nano- and quantum devices have increasingly complex 3D structure. As the dimensions of these devices shrink to the nanoscale, their performance is often governed by interface quality or precise chemical or dopant composition. Here, we present the first phase-sensitive extreme ultraviolet imaging reflectometer. It combines the excellent phase stability of coherent high-harmonic sources, the unique chemical sensitivity of extreme ultraviolet reflectometry, and state-of-the-art ptychography imaging algorithms. This tabletop microscope can nondestructively probe surface topography, layer thicknesses, and interface quality, as well as dopant concentrations and profiles. High-fidelity imaging was achieved by implementing variable-angle ptychographic imaging, by using total variation regularization to mitigate noise and artifacts in the reconstructed image, and by using a high-brightness, high-harmonic source with excellent intensity and wavefront stability. We validate our measurements through multiscale, multimodal imaging to show that this technique has unique advantages compared with other techniques based on electron and scanning probe microscopies.

Nondestructive Measurements of the Mechanical and Structural Properties of Nanostructured Metalattices

Metalattices are artificial 3D solids, periodic on sub-100 nm length scales, that enable the functional properties of materials to be tuned. However, because of their complex structure, predicting and characterizing their properties is challenging. Here we demonstrate the first nondestructive measurements of the mechanical and structural properties of metalattices with feature sizes down to 14 nm. By monitoring the time-dependent diffraction of short wavelength light from laser-excited acoustic waves in the metalattices, we extract their acoustic dispersion, Young's modulus, filling fraction, and thicknesses. Our measurements are in excellent agreement with macroscopic predictions and potentially destructive techniques such as nanoindentation and scanning electron microscopy, with increased accuracy over larger areas. This is interesting because the transport properties of these metalattices do not obey bulk predictions. Finally, this approach is the only way to validate the filling fraction of metalattices over macroscopic areas. These combined capabilities can enable accurate synthesis of nanoenhanced materials.

Direct light-induced spin transfer between different elements in a spintronic Heusler material via femtosecond laser excitation

Heusler compounds are exciting materials for future spintronics applications because they display a wide range of tunable electronic and magnetic interactions. Here, we use a femtosecond laser to directly transfer spin polarization from one element to another in a half-metallic Heusler material, Co₂MnGe. This spin transfer initiates as soon as light is incident on the material, demonstrating spatial transfer of angular momentum between neighboring atomic sites on time scales < 10 fs. Using ultrafast high harmonic pulses to simultaneously and independently probe the magnetic state of two elements during laser excitation, we find that the magnetization of Co is enhanced, while that of Mn rapidly quenches. Density functional theory calculations show that the optical excitation directly transfers spin from one magnetic sublattice to another through preferred spin-polarized excitation pathways. This direct manipulation of spins via light provides a path toward spintronic devices that can operate on few-femtosecond or faster time scales.

Generation of extreme-ultraviolet beams with time-varying orbital angular momentum

Light fields carrying orbital angular momentum (OAM) provide powerful capabilities for applications in optical communications, microscopy, quantum optics, and microparticle manipulation. We introduce a property of light beams, manifested as a temporal OAM variation along a pulse: the self-torque of light. Although self-torque is found in diverse physical systems (i.e., electrodynamics and general relativity), it was not realized that light could possess such a property. We demonstrate that extreme-ultraviolet self-torqued beams arise in high-harmonic generation driven by time-delayed pulses with different OAM. We monitor the self-torque of extreme-ultraviolet beams through their azimuthal frequency chirp. This class of dynamic-OAM beams provides the ability for controlling magnetic, topological, and quantum excitations and for manipulating molecules and nanostructures on their natural time and length scales.

Conservation of Torus-knot Angular Momentum in High-order Harmonic Generation

High-order harmonic generation stands as a unique nonlinear optical up-conversion process, mediated by a laser-driven electron recollision mechanism, which has been shown to conserve energy, linear momentum, and spin and orbital angular momentum. Here, we present theoretical simulations that demonstrate that this process also conserves a mixture of the latter, the torus-knot angular momentum J_{γ}, by producing high-order harmonics with driving pulses that are invariant under coordinated rotations. We demonstrate that the charge J_{γ} of the emitted harmonics scales linearly with the harmonic order, and that this conservation law is imprinted onto the polarization distribution of the emitted spiral of attosecond pulses. We also demonstrate how the nonperturbative physics of high-order harmonic generation affect the torus-knot angular momentum of the harmonics, and we show that this configuration harnesses the spin selection rules to channel the full yield of each harmonic into a single mode of controllable orbital angular momentum.

Full-field imaging of thermal and acoustic dynamics in an individual nanostructure using tabletop high harmonic beams

Imaging charge, spin, and energy flow in materials is a current grand challenge that is relevant to a host of nanoenhanced systems, including thermoelectric, photovoltaic, electronic, and spin devices. Ultrafast coherent x-ray sources enable functional imaging on nanometer length and femtosecond timescales particularly when combined with advances in coherent imaging techniques. Here, we combine ptychographic coherent diffractive imaging with an extreme ultraviolet high harmonic light source to directly visualize the complex thermal and acoustic response of an individual nanoscale antenna after impulsive heating by a femtosecond laser. We directly image the deformations induced in both the nickel tapered nanoantenna and the silicon substrate and see the lowest-order generalized Lamb wave that is partially confined to a uniform nanoantenna. The resolution achieved-sub-100 nm transverse and 0.5-Å axial spatial resolution, combined with ≈10-fs temporal resolution-represents a significant advance in full-field dynamic imaging capabilities. The tapered nanoantenna is sufficiently complex that a full simulation of the dynamic response would require enormous computational power. We therefore use our data to benchmark approximate models and achieve excellent agreement between theory and experiment. In the future, this work will enable three-dimensional functional imaging of opaque materials and nanostructures that are sufficiently complex that their functional properties cannot be predicted.

Ionization-assisted spatiotemporal localization in gas-filled capillaries

We demonstrate numerically and experimentally that intense pulses propagating in gas-filled capillaries can undergo localization in space and time due to strong plasma defocusing. This phenomenon can occur below or above the self-focusing threshold P_cr as a result of ionization-induced refraction that excites higher-order modes. The constructive interference of higher-order modes leads to spatiotemporal localization and resurgence of the intensity. Simulations show that this confinement is more prominent at shorter wavelength pulses and for smaller capillary diameters. Experiments with ultraviolet pulses show evidence that this ionization-induced refocusing appears below P_cr and thus represents a mechanism for spatiotemporal confinement without self-focusing.

Single-shot 3D coherent diffractive imaging of core-shell nanoparticles with elemental specificity

We report 3D coherent diffractive imaging (CDI) of Au/Pd core-shell nanoparticles with 6.1 nm spatial resolution with elemental specificity. We measured single-shot diffraction patterns of the nanoparticles using intense x-ray free electron laser pulses. By exploiting the curvature of the Ewald sphere and the symmetry of the nanoparticle, we reconstructed the 3D electron density of 34 core-shell structures from these diffraction patterns. To extract 3D structural information beyond the diffraction signal, we implemented a super-resolution technique by taking advantage of CDI’s quantitative reconstruction capabilities. We used high-resolution model fitting to determine the Au core size and the Pd shell thickness to be 65.0 ± 1.0 nm and 4.0 ± 0.5 nm, respectively. We also identified the 3D elemental distribution inside the nanoparticles with an accuracy of 3%. To further examine the model fitting procedure, we simulated noisy diffraction patterns from a Au/Pd core-shell model and a solid Au model and confirmed the validity of the method. We anticipate this super-resolution CDI method can be generally used for quantitative 3D imaging of symmetrical nanostructures with elemental specificity.

Colloidal crystal order and structure revealed by tabletop extreme ultraviolet scattering and coherent diffractive imaging

Colloidal crystals with specific electronic, optical, magnetic, vibrational properties, can be rationally designed by controlling fundamental parameters such as chemical composition, scale, periodicity and lattice symmetry. In particular, silica nanospheres -which assemble to form colloidal crystals- are ideal for this purpose, because of the ability to infiltrate their templates with semiconductors or metals. However characterization of these crystals is often limited to techniques such as grazing incidence small-angle scattering that provide only global structural information and also often require synchrotron sources. Here we demonstrate small-angle Bragg scattering from nanostructured materials using a tabletop-scale setup based on high-harmonic generation, to reveal important information about the local order of nanosphere grains, separated by grain boundaries and discontinuities. We also apply full-field quantitative ptychographic imaging to visualize the extended structure of a silica close-packed nanosphere multilayer, with thickness information encoded in the phase. These combined techniques allow us to simultaneously characterize the silica nanospheres size, their symmetry and distribution within single colloidal crystal grains, the local arrangement of nearest-neighbor grains, as well as to quantitatively determine the number of layers within the sample. Key to this advance is the good match between the high harmonic wavelength used (13.5nm) and the high transmission, high scattering efficiency, and low sample damage of the silica colloidal crystal at this wavelength. As a result, the relevant distances in the sample - namely, the interparticle distance (≈124nm) and the colloidal grains local arrangement (≈1μm) - can be investigated with Bragg coherent EUV scatterometry and ptychographic imaging within the same experiment simply by tuning the EUV spot size at the sample plane (5μm and 15μm respectively). In addition, the high spatial coherence of high harmonics light, combined with advances in imaging techniques, makes it possible to image near-periodic structures quantitatively and nondestructively, and enables the observation of the extended order of quasi-periodic colloidal crystals, with a spatial resolution better than 20nm. In the future, by harnessing the high time-resolution of tabletop high harmonics, this technique can be extended to dynamically image the three-dimensional electronic, magnetic, and transport properties of functional nanosystems.

Near- and Extended-Edge X-Ray-Absorption Fine-Structure Spectroscopy Using Ultrafast Coherent High-Order Harmonic Supercontinua

Recent advances in high-order harmonic generation have made it possible to use a tabletop-scale setup to produce spatially and temporally coherent beams of light with bandwidth spanning 12 octaves, from the ultraviolet up to x-ray photon energies >1.6  keV. Here we demonstrate the use of this light for x-ray-absorption spectroscopy at the K- and L-absorption edges of solids at photon energies near 1 keV. We also report x-ray-absorption spectroscopy in the water window spectral region (284-543 eV) using a high flux high-order harmonic generation x-ray supercontinuum with 10^{9}  photons/s in 1% bandwidth, 3 orders of magnitude larger than has previously been possible using tabletop sources. Since this x-ray radiation emerges as a single attosecond-to-femtosecond pulse with peak brightness exceeding 10^{26}  photons/s/mrad^{2}/mm^{2}/1% bandwidth, these novel coherent x-ray sources are ideal for probing the fastest molecular and materials processes on femtosecond-to-attosecond time scales and picometer length scales.

Critical behavior within 20 fs drives the out-of-equilibrium laser-induced magnetic phase transition in nickel

It has long been known that ferromagnets undergo a phase transition from ferromagnetic to paramagnetic at the Curie temperature, associated with critical phenomena such as a divergence in the heat capacity. A ferromagnet can also be transiently demagnetized by heating it with an ultrafast laser pulse. However, to date, the connection between out-of-equilibrium and equilibrium phase transitions, or how fast the out-of-equilibrium phase transitions can proceed, was not known. By combining time- and angle-resolved photoemission with time-resolved transverse magneto-optical Kerr spectroscopies, we show that the same critical behavior also governs the ultrafast magnetic phase transition in nickel. This is evidenced by several observations. First, we observe a divergence of the transient heat capacity of the electron spin system preceding material demagnetization. Second, when the electron temperature is transiently driven above the Curie temperature, we observe an extremely rapid change in the material response: The spin system absorbs sufficient energy within the first 20 fs to subsequently proceed through the phase transition, whereas demagnetization and the collapse of the exchange splitting occur on much longer, fluence-independent time scales of ~176 fs. Third, we find that the transient electron temperature alone dictates the magnetic response. Our results are important because they connect the out-of-equilibrium material behavior to the strongly coupled equilibrium behavior and uncover a new time scale in the process of ultrafast demagnetization.

Controlling the polarization and vortex charge of attosecond high-harmonic beams via simultaneous spin-orbit momentum conservation

Optical interactions are governed by both spin and angular momentum conservation laws, which serve as a tool for controlling light-matter interactions or elucidating electron dynamics and structure of complex systems. Here, we uncover a form of simultaneous spin and orbital angular momentum conservation and show, theoretically and experimentally, that this phenomenon allows for unprecedented control over the divergence and polarization of extreme-ultraviolet vortex beams. High harmonics with spin and orbital angular momenta are produced, opening a novel regime of angular momentum conservation that allows for manipulation of the polarization of attosecond pulses-from linear to circular-and for the generation of circularly polarized vortices with tailored orbital angular momentum, including harmonic vortices with the same topological charge as the driving laser beam. Our work paves the way to ultrafast studies of chiral systems using high-harmonic beams with designer spin and orbital angular momentum.

Helicity-Selective Enhancement and Polarization Control of Attosecond High Harmonic Waveforms Driven by Bichromatic Circularly Polarized Laser Fields

High harmonics driven by two-color counterrotating circularly polarized laser fields are a unique source of bright, circularly polarized, extreme ultraviolet, and soft x-ray beams, where the individual harmonics themselves are completely circularly polarized. Here, we demonstrate the ability to preferentially select either the right or left circularly polarized harmonics simply by adjusting the relative intensity ratio of the bichromatic circularly polarized driving laser field. In the frequency domain, this significantly enhances the harmonic orders that rotate in the same direction as the higher-intensity driving laser. In the time domain, this helicity-dependent enhancement corresponds to control over the polarization of the resulting attosecond waveforms. This helicity control enables the generation of circularly polarized high harmonics with a user-defined polarization of the underlying attosecond bursts. In the future, this technique should allow for the production of bright highly elliptical harmonic supercontinua as well as the generation of isolated elliptically polarized attosecond pulses.

Isolated broadband attosecond pulse generation with near- and mid-infrared driver pulses via time-gated phase matching

We present a theoretical analysis of the time-gated phase matching (ionization gating) mechanism in high-order harmonic generation for the isolation of attosecond pulses at near-infrared and mid-infrared driver wavelengths, for both few-cycle and multi-cycle driving laser pulses. Results of our high harmonic generation and three-dimensional propagation simulations show that broadband isolated pulses spanning from the extreme-ultraviolet well into the soft X-ray region of the spectrum can be generated for both few-cycle and multi-cycle laser pulses. We demonstrate the key role of absorption and group velocity matching for generating bright, isolated, attosecond pulses using long wavelength multi-cycle pulses. Finally, we show that this technique is robust against carrier-envelope phase and peak intensity variations.

Phase matching of noncollinear sum and difference frequency high harmonic generation above and below the critical ionization level

We investigate the macroscopic physics of noncollinear high harmonic generation (HHG) at high pressures. We make the first experimental demonstration of phase matching of noncollinear high-order-difference-frequency generation at ionization fractions above the critical ionization level, which normally sets an upper limit on the achievable cutoff photon energies. Additionally, we show that noncollinear high-order-sum-frequency generation requires much higher pressures for phase matching than single-beam HHG does, which mitigates the short interaction region in this geometry. We also dramatically increase the experimentally realized cutoff energy of noncollinear circularly polarized HHG, reaching photon energies of 90 eV. Finally, we achieve complete angular separation of high harmonic orders without the use of a spectrometer.

Full Characterization of the Mechanical Properties of 11-50 nm Ultrathin Films: Influence of Network Connectivity on the Poisson's Ratio

Precise characterization of the mechanical properties of ultrathin films is of paramount importance for both a fundamental understanding of nanoscale materials and for continued scaling and improvement of nanotechnology. In this work, we use coherent extreme ultraviolet beams to characterize the full elastic tensor of isotropic ultrathin films down to 11 nm in thickness. We simultaneously extract the Young's modulus and Poisson's ratio of low-k a-SiC:H films with varying degrees of hardness and average network connectivity in a single measurement. Contrary to past assumptions, we find that the Poisson's ratio of such films is not constant but rather can significantly increase from 0.25 to >0.4 for a network connectivity below a critical value of ∼2.5. Physically, the strong hydrogenation required to decrease the dielectric constant k results in bond breaking, lowering the network connectivity, and Young's modulus of the material but also decreases the compressibility of the film. This new understanding of ultrathin films demonstrates that coherent EUV beams present a new nanometrology capability that can probe a wide range of novel complex materials not accessible using traditional approaches.

Uncovering Highly-Excited State Mixing in Acetone Using Ultrafast VUV Pulses and Coincidence Imaging Techniques

Understanding the ultrafast dynamics of highly excited electronic states of small molecules is critical for a better understanding of atmospheric and astrophysical processes, as well as for designing coherent control strategies for manipulating chemical dynamics. In highly excited states, nonadiabatic coupling, electron-electron interactions, and the high density of states govern dynamics. However, these states are computationally and experimentally challenging to access. Fortunately, new sources of ultrafast vacuum ultraviolet pulses, in combination with electron-ion coincidence spectroscopies, provide new tools to unravel the complex electronic landscape. Here we report time-resolved photoelectron-photoion coincidence experiments using 8 eV pump photons to study the highly excited states of acetone. We uncover for the first time direct evidence that the resulting excited state consists of a mixture of both n_y → 3p and π → π* character, which decays with a time constant of 330 fs. In the future, this approach can inform models of VUV photochemistry and aid in designing coherent control strategies for manipulating chemical reactions.

Self-amplified photo-induced gap quenching in a correlated electron material

Capturing the dynamic electronic band structure of a correlated material presents a powerful capability for uncovering the complex couplings between the electronic and structural degrees of freedom. When combined with ultrafast laser excitation, new phases of matter can result, since far-from-equilibrium excited states are instantaneously populated. Here, we elucidate a general relation between ultrafast non-equilibrium electron dynamics and the size of the characteristic energy gap in a correlated electron material. We show that carrier multiplication via impact ionization can be one of the most important processes in a gapped material, and that the speed of carrier multiplication critically depends on the size of the energy gap. In the case of the charge-density wave material 1T-TiSe₂, our data indicate that carrier multiplication and gap dynamics mutually amplify each other, which explains-on a microscopic level-the extremely fast response of this material to ultrafast optical excitation.

Controlling Nonsequential Double Ionization in Two-Color Circularly Polarized Femtosecond Laser Fields

Atoms undergoing strong-field ionization in two-color circularly polarized femtosecond laser fields exhibit unique two-dimensional photoelectron trajectories and can emit bright circularly polarized extreme ultraviolet and soft-x-ray beams. In this Letter, we present the first experimental observation of nonsequential double ionization in these tailored laser fields. Moreover, we can enhance or suppress nonsequential double ionization by changing the intensity ratio and helicity of the two driving laser fields to maximize or minimize high-energy electron-ion rescattering. Our experimental results are explained through classical simulations, which also provide insight into how to optimize the generation of circularly polarized high harmonic beams.

Lorentz drift compensation in high harmonic generation in the soft and hard X-ray regions of the spectrum

We present a semi-classical study of the effects of the Lorentz force on electrons during high harmonic generation in the soft and hard X-ray regions driven by near- and mid-infrared lasers with wavelengths from 0.8 to 20 μm, and at intensities below 10¹⁵ W/cm². The transverse extent of the longitudinal Lorentz drift is compared for both Gaussian focus and waveguide geometries. Both geometries exhibit a longitudinal electric field component that cancels the magnetic Lorentz drift in some regions of the focus, once each full optical cycle. We show that the Lorentz force contributes a super-Gaussian scaling which acts in addition to the dominant high harmonic flux scaling of λ^-(5-6) due to quantum diffusion. We predict that the high harmonic yield will be reduced for driving wavelengths > 6 μm, and that the presence of dynamic spatial mode asymmetries results in the generation of both even and odd harmonic orders. Remarkably, we show that under realistic conditions, the recollision process can be controlled and does not shut off completely even for wavelengths >10 μm and recollision energies greater than 15 keV.

Quantitative Chemically Specific Coherent Diffractive Imaging of Reactions at Buried Interfaces with Few Nanometer Precision

We demonstrate quantitative, chemically specific imaging of buried nanostructures, including oxidation and diffusion reactions at buried interfaces, using nondestructive tabletop extreme ultraviolet (EUV) coherent diffractive imaging (CDI). Copper nanostructures inlaid in SiO2 are coated with 100 nm of aluminum, which is opaque to visible light and thick enough that neither visible microscopy nor atomic force microscopy can image the buried interface. Short wavelength high harmonic beams can penetrate the aluminum layer, yielding high-contrast images of the buried structures. Quantitative analysis shows that the reflected EUV light is extremely sensitive to the formation of multiple oxide layers, as well as interdiffusion of materials occurring at the metal-metal and metal-insulator boundaries deep within the nanostructure with few nanometers precision.

Nondestructive Measurement of the Evolution of Layer-Specific Mechanical Properties in Sub-10 nm Bilayer Films

We use short wavelength extreme ultraviolet light to independently measure the mechanical properties of disparate layers within a bilayer film for the first time, with single-monolayer sensitivity. We show that in Ni/Ta nanostructured systems, while their density ratio is not meaningfully changed from that expected in bulk, their elastic properties are significantly modified, where nickel softens while tantalum stiffens, relative to their bulk counterparts. In particular, the presence or absence of the Ta capping layer influences the mechanical properties of the Ni film. This nondestructive nanomechanical measurement technique represents the first approach to date able to distinguish the properties of composite materials well below 100 nm in thickness. This capability is critical for understanding and optimizing the strength, flexibility and reliability of materials in a host of nanostructured electronic, photovoltaic, and thermoelectric devices.

Ptychographic hyperspectral spectromicroscopy with an extreme ultraviolet high harmonic comb

We report a proof-of-principle demonstration of a new scheme of spectromicroscopy in the extreme ultraviolet (EUV) spectral range, where the spectral response of the sample at different wavelengths is imaged simultaneously. This scheme is enabled by combining ptychographic information multiplexing (PIM) with a tabletop EUV source based on high harmonic generation, where four spectrally narrow harmonics near 30 nm form a spectral comb structure. Extending PIM from previously demonstrated visible wavelengths to the EUV/X-ray wavelengths promises much higher spatial resolution and a more powerful spectral contrast mechanism, making PIM an attractive spectromicroscopy method in both microscopy and spectroscopy aspects. In addition to spectromicroscopy, this method images the multicolor EUV beam in situ, making this a powerful beam characterization technique. In contrast to other methods, the techniques described here use no hardware to separate wavelengths, leading to efficient use of the EUV radiation.

Materials Properties and Solvated Electron Dynamics of Isolated Nanoparticles and Nanodroplets Probed with Ultrafast Extreme Ultraviolet Beams

We present ultrafast photoemission measurements of isolated nanoparticles in vacuum using extreme ultraviolet (EUV) light produced through high harmonic generation. Surface-selective static EUV photoemission measurements were performed on nanoparticles with a wide array of compositions, ranging from ionic crystals to nanodroplets of organic material. We find that the total photoelectron yield varies greatly with nanoparticle composition and provides insight into material properties such as the electron mean free path and effective mass. Additionally, we conduct time-resolved photoelectron yield measurements of isolated oleylamine nanodroplets, observing that EUV photons can create solvated electrons in liquid nanodroplets. Using photoemission from a time-delayed 790 nm pulse, we observe that a solvated electron is produced in an excited state and subsequently relaxes to its ground state with a lifetime of 151 ± 31 fs. This work demonstrates that femotosecond EUV photoemission is a versatile surface-sensitive probe of the properties and ultrafast dynamics of isolated nanoparticles.

Bright circularly polarized soft X-ray high harmonics for X-ray magnetic circular dichroism

We demonstrate, to our knowledge, the first bright circularly polarized high-harmonic beams in the soft X-ray region of the electromagnetic spectrum, and use them to implement X-ray magnetic circular dichroism measurements in a tabletop-scale setup. Using counterrotating circularly polarized laser fields at 1.3 and 0.79 µm, we generate circularly polarized harmonics with photon energies exceeding 160 eV. The harmonic spectra emerge as a sequence of closely spaced pairs of left and right circularly polarized peaks, with energies determined by conservation of energy and spin angular momentum. We explain the single-atom and macroscopic physics by identifying the dominant electron quantum trajectories and optimal phase-matching conditions. The first advanced phase-matched propagation simulations for circularly polarized harmonics reveal the influence of the finite phase-matching temporal window on the spectrum, as well as the unique polarization-shaped attosecond pulse train. Finally, we use, to our knowledge, the first tabletop X-ray magnetic circular dichroism measurements at the N4,5 absorption edges of Gd to validate the high degree of circularity, brightness, and stability of this light source. These results demonstrate the feasibility of manipulating the polarization, spectrum, and temporal shape of high harmonics in the soft X-ray region by manipulating the driving laser waveform.

Attosecond Coherent Control of Single and Double Photoionization in Argon

Ultrafast high harmonic beams provide new opportunities for coherently controlling excitation and ionization processes in atoms, molecules, and materials on attosecond time scales by employing multiphoton two-pathway electron-wave-packet quantum interferences. Here we use spectrally tailored and frequency tuned vacuum and extreme ultraviolet harmonic combs, together with two phase-locked infrared laser fields, to show how the total single and double photoionization yields of argon can be coherently modulated by controlling the relative phases of both optical and electronic-wave-packet quantum interferences. This Letter is the first to apply quantum control techniques to double photoionization, which is a fundamental process where a single, high-energy photon ionizes two electrons simultaneously from an atom.

Solvents effects on charge transfer from quantum dots

To predict and understand the performance of nanodevices in different environments, the influence of the solvent must be explicitly understood. In this Communication, this important but largely unexplored question is addressed through a comparison of quantum dot charge transfer processes occurring in both liquid phase and in vacuum. By comparing solution phase transient absorption spectroscopy and gas-phase photoelectron spectroscopy, we show that hexane, a common nonpolar solvent for quantum dots, has negligible influence on charge transfer dynamics. Our experimental results, supported by insights from theory, indicate that the reorganization energy of nonpolar solvents plays a minimal role in the energy landscape of charge transfer in quantum dot devices. Thus, this study demonstrates that measurements conducted in nonpolar solvents can indeed provide insight into nanodevice performance in a wide variety of environments.

Mapping nanoscale absorption of femtosecond laser pulses using plasma explosion imaging

We make direct observations of localized light absorption in a single nanostructure irradiated by a strong femtosecond laser field, by developing and applying a technique that we refer to as plasma explosion imaging. By imaging the photoion momentum distribution resulting from plasma formation in a laser-irradiated nanostructure, we map the spatial location of the highly localized plasma and thereby image the nanoscale light absorption. Our method probes individual, isolated nanoparticles in vacuum, which allows us to observe how small variations in the composition, shape, and orientation of the nanostructures lead to vastly different light absorption. Here, we study four different nanoparticle samples with overall dimensions of ∼100 nm and find that each sample exhibits distinct light absorption mechanisms despite their similar size. Specifically, we observe subwavelength focusing in single NaCl crystals, symmetric absorption in TiO2 aggregates, surface enhancement in dielectric particles containing a single gold nanoparticle, and interparticle hot spots in dielectric particles containing multiple smaller gold nanoparticles. These observations demonstrate how plasma explosion imaging directly reveals the diverse ways in which nanoparticles respond to strong laser fields, a process that is notoriously challenging to model because of the rapid evolution of materials properties that takes place on the femtosecond time scale as a solid nanostructure is transformed into a dense plasma.

Observation and control of shock waves in individual nanoplasmas

Using an apparatus that images the momentum distribution of individual, isolated 100-nm-scale plasmas, we make the first experimental observation of shock waves in nanoplasmas. We demonstrate that the introduction of a heating pulse prior to the main laser pulse increases the intensity of the shock wave, producing a strong burst of quasimonoenergetic ions with an energy spread of less than 15%. Numerical hydrodynamic calculations confirm the appearance of accelerating shock waves and provide a mechanism for the generation and control of these shock waves. This observation of distinct shock waves in dense plasmas enables the control, study, and exploitation of nanoscale shock phenomena with tabletop-scale lasers.

High flux coherent super-continuum soft X-ray source driven by a single-stage, 10mJ, Ti:sapphire amplifier-pumped OPA

We demonstrate the highest flux tabletop source of coherent soft X-rays to date, driven by a single-stage 10 mJ Ti:sapphire regenerative amplifier at 1 kHz. We first down-convert the laser to 1.3 µm using a parametric amplifier, before up-converting it to soft X-rays using high harmonic generation in a high-pressure, phase matched, hollow waveguide geometry. The resulting optimally phase matched broadband spectrum extends to 200 eV, with a soft X-ray photon flux of > 10(6) photons/pulse/1% bandwidth at 1 kHz, corresponding to > 10(9) photons/s/1% bandwidth, or approximately a three order-of-magnitude increase compared with past work. Finally, using this broad bandwidth X-ray source, we demonstrate X-ray absorption spectroscopy of multiple elements and transitions in molecules in a single spectrum, with a spectral resolution of 0.25 eV, and with the ability to resolve the near edge fine structure.